Strain - ε

Strain is the "deformation of a solid due to stress" - change in dimension divided by theoriginal value of the dimension - and can be expressed as

ε = dL / L (1)

where

ε = strain (m/m, in/in)

dL = elongation or compression (offset) of object (m, in)

L = length of object (m, in)

Stress - σStress is force per unit area and can be expressed as

σ=F/A (2)

where

σ = stress (N/m2, lb/in2, psi)

F = applied force (N, lb)

A = stress area of object (m2, in2)

 tensile stress - stress that tends to stretch or lengthen the material - acts normal to the stressed area  compressible stress - stress that tends to compress or shorten the material - acts normal to the stressed area  shearing stress - stress that tends to shear the material - acts in plane to the stressed area at right-angles to compressible or tensile stressYoung's Modulus - Tensile Modulus, Modulus of Elasticity - EYoung's modulus can be expressed as

E = stress / strain

= σ/ε

= (F / A) / (dL / L) (3)

where

E = Young's Modulus of Elasticity (N/m2, lb/in2, psi)

 named after the 18th-century English physician and physicist Thomas YoungElasticityElasticity is a property of an object or material indicating how it will restore it to its originalshape after distortion.

A spring is an example of an elastic object - when stretched, it exerts a restoring force whichtends to bring it back to its original length. This restoring force is in general proportional tothe stretch described by Hooke's Law.

Hooke's LawIt takes about twice as much force to stretch a spring twice as far. That linear dependence ofdisplacement upon the stretching force is called Hooke's law and can be expressed as

Fs = -k dL (4)

where

Fs = force in the spring (N)

k = spring constant (N/m)

dL = elongation of the spring (m)

Note that Hooke's Law can also be applied to materials undergoing three dimensional stress(triaxial loading).

Yield strength - σyYield strength is defined in engineering as the amount of stress (Yield point) that a materialcan undergo before moving from elastic deformation into plastic deformation.

 Yielding - a material deforms permanently

The Yield Point is in mild- or medium-carbon steel the stress at which a marked increase indeformation occurs without increase in load. In other steels and in nonferrous metals thisphenomenon is not observed.

Ultimate Tensile Strength - σu

The Ultimate Tensile Strength - UTS - of a material is the limit stress at which the materialactually breaks, with a sudden release of the stored elastic energy.